Using the definition of the derivative as a limit, show that the derivative of
The slope of a line tangent to at any point
If the slope (or instantaneous rate of change) at a particular
This is one form of the 'definition of the derivative' (informally known as Hana's Method).
In order to evaluate this limit, we need to find an Algebraic way to cancel out the
Find a common denominator in the numerator, expand and combine like terms:
Factor the numerator, then cancel out the
Since there is no longer and